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Table 1 Global dynamics of system (1) with (2) summarized from Sects. 3, 4, 5 and 6

From: Modeling plant virus propagation with Filippov control

Case Condition Equilibrium Main result
\(Y_{c}< Y_{3}^{*}< Y_{2}^{*}< Y_{1}^{*}\) \(I_{c}< g_{4}< g_{5}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{R}\) (I)
\(Y_{c}< Y_{3}^{*}< Y_{2}^{*}< Y_{1}^{*}\) \(g_{4}< I_{c}< g_{5}\), \(I_{c}<\min \{I_{3}^{*}, g_{5}\}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{R}\) (I)
\(Y_{c}< Y_{3}^{*}< Y_{2}^{*}< Y_{1}^{*}\) \(g_{4}< I_{c}< g_{5} \), \(I_{3}^{*}< I_{c}< g_{5}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{V}\), \(E_{p2}\) (II)
\(Y_{c}< Y_{3}^{*}< Y_{2}^{*}< Y_{1}^{*}\) \(g_{4}< g_{5}< I_{c}\), \(I_{c}<\max \{I_{3}^{*}, g_{5}\}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{2}^{R}\) (I)
\(Y_{c}< Y_{3}^{*}< Y_{2}^{*}< Y_{1}^{*}\) \(g_{4}< g_{5}< I_{c}\), \(\max \{I_{3}^{*}, g_{5}\}< I_{c}< I_{1}^{*}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{V} E_{p2}\) (II)
\(Y_{c}< Y_{3}^{*}< Y_{2}^{*}< Y_{1}^{*}\) \(g_{4}< g_{5}< I_{c}\), \(I_{c}>I_{1}^{*}\) \(E_{1}^{R}\), \(E_{2}^{V}\), \(E_{3}^{V}\) (III)
\(Y_{3}^{*}< Y_{c}< Y_{2}^{*}< Y_{1}^{*}\) \(I_{c}< g_{4}< g_{5}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{V}\), \(E_{p3}\) (I)
\(Y_{3}^{*}< Y_{c}< Y_{2}^{*}< Y_{1}^{*}\) \(g_{4}< I_{c}< g_{5}\), \(I_{c}< g_{3}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{V}\), \(E_{c}\) (II)
\(Y_{3}^{*}< Y_{c}< Y_{2}^{*}< Y_{1}^{*}\) \(g_{4}< I_{c}< g_{4}\), \(I_{c}>g_{3}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{V}\), \(E_{p2}\) (II)
\(Y_{3}^{*}< Y_{c}< Y_{2}^{*}< Y_{1}^{*}\) \(g_{4}< g_{5}< I_{c}\), \(I_{c}< I_{1}^{*}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{V}\), \(E_{p2}\) (II)
\(Y_{3}^{*}< Y_{c}< Y_{2}^{*}< Y_{1}^{*}\) \(g_{4}< g_{5}< I_{c}\), \(I_{c}>I_{1}^{*}\) \(E_{1}^{R}\), \(E_{2}^{V}\), \(E_{3}^{V}\) (III)
\(Y_{3}^{*}< Y_{2}^{*}< Y_{c}< Y_{1}^{*}\) \(I_{c}< g_{4}< g_{5}\), \(I_{c}< I_{2}^{*}\) \(E_{1}^{V}\), \(E_{2}^{R}\), \(E_{3}^{V}\) (I)
\(Y_{3}^{*}< Y_{2}^{*}< Y_{c}< Y_{1}^{*}\) \(I_{c}< g_{4}< g_{5}\), \(I_{c}< I_{2}^{*}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{V}\), \(E_{p1}\) (II)
\(Y_{3}^{*}< Y_{2}^{*}< Y_{c}< Y_{1}^{*}\) \(g_{4}< I_{c}< g_{5}\), \(I_{c}< g_{1}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{V}\), \(E_{p1}\) (II)
\(Y_{3}^{*}< Y_{2}^{*}< Y_{c}< Y_{1}^{*}\) \(g_{4}< I_{c}< g_{5}\), \(g_{1}< I_{c}< g_{3}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{V}\), \(E_{c}\) (II)
\(Y_{3}^{*}< Y_{2}^{*}< Y_{c}< Y_{1}^{*}\) \(g_{4}< I_{c}< g_{5}\), \(I_{c}>g_{3}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{V}\), \(E_{p2}\) (II)
\(Y_{3}^{*}< Y_{2}^{*}< Y_{c}< Y_{1}^{*}\) \(g_{4}< g_{5}< I_{c}\), \(I_{c}< I_{1}^{*}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{V}\), \(E_{p2}\) (II)
\(Y_{3}^{*}< Y_{2}^{*}< Y_{c}< Y_{1}^{*}\) \(g_{4}< g_{5}< I_{c}\), \(I_{c}>I_{1}^{*}\) \(E_{1}^{R}\), \(E_{2}^{V}\), \(E_{3}^{V}\) (III)
\(Y_{3}^{*}< Y_{2}^{*}< Y_{1}^{*}< Y_{c}\) \(I_{c}< g_{4}< g_{5}\), \(I_{c}< I_{2}^{*}\) \(E_{1}^{V}\), \(E_{2}^{R}\), \(E_{3}^{V}\) (I)
\(Y_{3}^{*}< Y_{2}^{*}< Y_{1}^{*}< Y_{c}\) \(I_{c}< g_{4}< g_{5}\), \(I_{2}^{*}< I_{c}<\min \{I_{1}^{*}, g_{4}\}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{V}\), \(E_{p1}\) (II)
\(Y_{3}^{*}< Y_{2}^{*}< Y_{1}^{*}< Y_{c}\) \(I_{c}< g_{4}< g_{5}\), \(I_{1}^{*}< I_{c}< g_{4}\) \(E_{1}^{R}\), \(E_{2}^{V}\), \(E_{3}^{V}\) (III)
\(Y_{3}^{*}< Y_{2}^{*}< Y_{1}^{*}< Y_{c}\) \(g_{4}< I_{c}< g_{5}\), \(g_{4}< I_{c}<\min \{I_{1}^{*}, g_{5}\}\) \(E_{1}^{V}\), \(E_{2}^{V}\), \(E_{3}^{V}\), \(E_{p1}\) (II)
\(Y_{3}^{*}< Y_{2}^{*}< Y_{1}^{*}< Y_{c}\) \(g_{4}< I_{c}< g_{5}\), \(\max \{I_{1}^{*}, g_{4}\}< I_{c}< g_{5}\) \(E_{1}^{R}\), \(E_{2}^{V}\), \(E_{3}^{V}\) (III)
\(Y_{3}^{*}< Y_{2}^{*}< Y_{1}^{*}< Y_{c}\) \(g_{4}< g_{5}< I_{c}\) \(E_{1}^{R}\), \(E_{2}^{V}\), \(E_{3}^{V}\) (III)